Twitter has inspired some of the most creative quantitive apps on the market. Here is a list of these really neat twitter apps with breif descriptions of what they are about.

TwitterFall
Twitterfall is a Twitter client specialising in real-time tweet searches. New tweets fall into the page.
Twitterfall has a huge feature list and there are many actions that can't be done on other clients.
Twitterfall was written by x5315 and Jalada. The name was coined by Chris Northwood. Twitterfall is a collection of Erlang, JQuery, Google Maps and Language APIs, Comet Push Technology and Twitter.
Some of these Features include Qrait Inegration, Twitlonger Support, Excluding Services, Link Expander, Trend Information, Conversation Viewing, Panel Collapsing, User Details, Picture Preview, Excluding Terms, Excluding Users, Speed Setting, Fall Size Setting and many more.

Klout - The Standard For Influence
WHAT IS INFLUENCE?
Influence is the ability to drive action. When you share something on social media or in real life and people respond, that’s influence. The more influential you are, the higher your Klout Score.
THE KLOUT SCORE
The Klout Score is a number between 1-100 that represents your influence. The more influential you are, the higher your Klout Score.
KLOUT SCORE SIGNALS
We use more than 400 signals from eight different networks to update your Klout Score every day*. Below is detailed description of how a Klout Score is determined.
The majority of the signals used to calculate the Klout Score are derived from combinations of attributes, such as the ratio of reactions you generate compared to the amount of content you share. For example, generating 100 retweets from 10 tweets will contribute more to your Score than generating 100 retweets from 1,000 tweets. We also consider factors such as how selective the people who interact with your content are. The more a person likes and retweets in a given day, the less each of those individual interactions contributes to another person's Score. Additionally, we value the engagement you drive from unique individuals. One-hundred retweets from 100 different people contribute more to your Score than do 100 retweets from a single person.
We know how important it is to maintain the integrity of the Klout Score, so we closely monitor activity across the signals we measure for inauthentic behaviors—spambots and the like. The Score will continue to evolve and improve as we add more networks and more signals.
* More than 12 billions signals measured every day.

Kred - Kred Story
See the Kred Influence and Outreach scores. Kred measures influence in communities connected by interests and affiliations.
Kred is composed of two scores: Influence and Outreach.
Kred scores reflect Trust and Generosity, the foundations of strong relationships. All of our Kred badges show Influence Scores on the upper left and Outreach Levels on the lower right.
Influence is the ability to inspire action. It is scored on a 1,000 point scale.
We measure Influence by assessing how frequently you are Retweeted, Replied, Mentioned and Followed on Twitter. If you connect your Facebook account to your Kred profile, you get Influence points when people interact with your content on your wall and the walls of others who have registered their Facebook account with Kred. Facebook interactions counted towards your Kred include Posts, Mentions, Likes, Shares and Event Invitations.
Outreach reflects generosity in engaging with others and helping them spread their message.
Since we believe that the capacity generosity is infinite, your Outreach score is cumulative and always increases. As of June 2012 the highest Outreach Level anyone has reached is 12, and we expect that higher levels will certainly be achieved in the future.
We measure Outreach on Twitter by your Retweets, Replies and Mentions of others. When your Facebook account is connected to your Kred profile, you get Outreach points for interactions on your own wall and the walls of others who have registered their Facebook account with Kred. Interactions counted towards Kred include Posts, Mentions, Comments and Likes.
Kred is the only influence measure to show how Twitter and Facebook activities contribute to your score. Visit your Activity Statement any time at http://kred.com/#activity.

Pulse of the Nation - U.S. Mood Throughout the Day inferred from Twitter
The plots were calculated using over 300 million tweets (Sep 2006 - Aug 2009) collected by MPI-SWS researchers [1], represented as density-preserving cartograms. This visualization includes both weekdays and weekends; in the future, will we create seperate maps for each. The mood of each tweet was inferred using ANEW word list [2] using the same basic methodology as previous work [3]. County area data were taken from the U.S. Census Bureau, and the base U.S. map was taken from Wikimedia Commons. User locations were inferred using the Google Maps API, and mapped into counties using PostGIS and U.S. county maps from the U.S. National Atlas. Mood colors were selected using Color Brewer 2.

TwitterMood - Mood On Twitter
nspiration:
One afternoon, we were all watching New York Times’ amazing super bowl visualization [1]. The team at NYT had collected all the super bowl related twitter messages they could find. Each tweet has a timestamp and many tweets have a location as well. These two pieces of information are somewhat boring when taken by themselves, but when combining thousands of messages, the result is just the opposite. A movie showing the location and frequency of tweets – from kick-off to the end of the game – tells a compelling story of the game itself as well as the nation watching.
A few days earlier, we had seen an exciting talk by Peter Dodds [2] describing how he was able to extract the emotional context of texts. As we were watching the super bowl visualization, we started discussing what the effect would be of plotting mood of millions of twitter messages to create a real time map that visually displayed the mood-swings of the US. What if the president could give a speech and immediately view the effect on his computer? Is it true the the east coast is more stressed out than the west coast? Are people happier in cities? Twittermood is a result of that discussion.
twitter data:
The twitter data is collected from the twitter gardenhose, which is stream containing a significant sample of all public twitter statuses. The gardenhose supplies about 1 800 000 messages per day [3].
mood:
We estimate the mood of all tweets for which the author has provided a location. The mood (valence) of each individual tweet is based on the Affective Norms for English Words (ANEW) data set [4], calculated as suggested in [5]. ANEW is a set of 1034 words, previously identified as bearing emotional weight (e.g. abuse, acceptance, accident). The mood of each word was estimated in a study at the University of Florida, where participants (college students), were shown lists of isolated words and asked to grade each word’s valence, arousal, and dominance level on an integer scale of 1-9.
location:
The location of each tweet is based on the self-reported location of each twitterer. In case a latitude and longitude is provided, this information is used. If a written location is provided (e.g. Boston, MA), the string is geocoded using the google maps API [6].
presentation:
The size of each circle is proportional to the logarithm of the number of tweets recorded at the location at the center of the circle. The color (from blue to yellow) of each circle is a function of the mood at the center, with yellow corresponding moods above average and blue below average. Circles are drawn at locations with at least 5 tweets.